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cynthiahqy / conformr-xmap-project

R Package for harmonising data of different classifications or aggregations into a single dataset
MIT License
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FAQ: What about many-to-many links? #50

Open cynthiahqy opened 1 year ago

cynthiahqy commented 1 year ago

I have a conjecture that many-to-many relations are just a collection or set of the one-to-one and one-to-many relation times, but haven't been able to fully prove it/convince myself yet. Most promising seems to checking whether you can always subdivide the graph / partition the incidence matrix into mutually exclusive sub-graphs/matrices for the one-to-one, one-to-many, many-to-one and many-to-many cases. Experimentally I found that depending on the order of conditions in case_when the ggplot2 node colourings changes, suggesting you can't achieve a "stable" colouring.

From a graph perspective, there are only two types of directed "outward" links possible in a lateral crosswalk, a source node will either have out degree of 1 (one-to-one) or out degree > 1 (one-to-many). On the target side, a given target node can have "in degree" of 1 (one-from-one or one-from-part), or "in degree > 1" (one-from-many).

Since there is a one-to-one correspondence between graphs and incidence matrices, is finding a contradiction in partitioning the matrix the same as showing the subgraphs we're looking for are not (edge?) disjoint?

image
cynthiahqy commented 1 year ago

Using the outgoing & incoming link properties you could potentially get subgraphs based on what transformations are implied by the map.

image

You could also have maps that were combinations that can't be divided further -- so it would be only meaningful to facet across one of the incoming OR outgoing link properties.

For example, the C+D link (ITA EUROPE 1) in the image can't be separated into an C type subgraph) because it involves EUROPE which is present in D.